Interesting and timely this; my friend had an issue with his this weekend where the compressor was overheating but his car wouldn't lower. It won't be the same for yours but we can use some of the same troubleshooting steps.
I'm not sure how your exhaust mod would stop it overheating, the heat is generated by it running too long but anyway, that's not the focus now.
If the car isn't raising but it is is pumping air, it's got to be one of a couple of issues. The air is escaping or (like Ray's car) it doesn't know where it is currently. Easiest thing to do is to use the tools that are built into the car as it's a free test. Get your 4x4 info screen up on the stereo and see what it thinks is happening.
Apologies if you know all of this already but it might help someone else out and I think it's often overlooked info.
Forgive the dust on my screen and have a look at the pic below to see (that I can brag about how mine is working

but also) what you are expecting to see.
Standard Height
View attachment 346413
This is a pictorial what the car "knows" so it's representative of the information it's makes decisions against.
For representation, I'll put a couple more pics here:
Off Road Height
View attachment 346414
You can see here that the centre line is above the wheel centres and that the wheel arches are depicted as being much higher.
Access Mode
View attachment 346415
Now the centre line is much lower and the wheel arches are only just above the tyre.
You might be thinking at this point "All very interesting but what am I doing with this info?" Well, here are a couple of pics from my friend's one:
Driver's Side Front
View attachment 346416
Sat at absolute full extension with the compressor running continuously and dead-heading itself with pressure then overheating, no matter what he did, it would NOT come down!
His 4x4 screen:
View attachment 346418
(Even more dust than mine)
Look at the OSF wheel in the pic, the car thinks that the wheel is buried in the arch lower than it needs to be even for Access Mode which means that it was pumping air into that corner like crazy to try and raise it to access height and level the car before it will lower the rest.
Simple enough, the height sensor arm had broken and the sensor was up making it think it was low and therefore trying to rectify an issue that didn't exist.
All that aside, it won't be the same issue for you but I'm trying to give you ideas on how to read the situation because people love to play 'Parts Darts' with these and sometimes the issue just isn't that bad. If you have the inverse of this and your car "thinks" it's raised on that corner, no matter what you do it won't level out. I like these tests because you can do them without getting dirty, worrying about the weather and you don't even
need to be sober (as long as you're on private land).
This is the part where you tell me you have an early car without the screen

You can use your diagnostic to get the voltages from the height sensors to work it out too but we'll cover that if we need to.